Greenland ice core records feature Dansgaard–Oeschger (D-O) events, which are abrupt warming episodes followed by gradual cooling during ice age climate. The three climate models used in this study (CCSM4, MPI-ESM, and HadCM3) show spontaneous self-sustained D-O-like oscillations (albeit with differences in amplitude, duration, and shape) in a remarkably similar, narrow window of carbon dioxide (CO2) concentration, roughly 185–230 ppm. This range matches atmospheric CO2 during Marine Isotopic Stage 3 (MIS 3: between 27.8 and 59.4 thousand of years BP, hereafter ka), a period when D-O events were most frequent. Insights from the three climate models point to North Atlantic (NA) sea-ice coverage as a key ingredient behind D-O type oscillations, which acts as a “tipping element.” Other climate state properties such as Mean Atlantic Meridional Overturning Circulation strength, global mean temperature and salinity gradient in the Atlantic Ocean do not determine whether D-O type behavior can occur in all three models.